# Stats: Multiplication Rule & Counting Rule Confusion

• shawnz1102
In summary, the conversation discusses two problems related to probability using a deck of cards. The first problem involves drawing three specific cards while the second problem involves drawing a specific number of a specific type of card. Both problems use different rules to solve, but it is possible to solve the second problem using the same rule as the first. However, it is important to consider the additional variable of the free card and its potential placement in the sequence of draws.
shawnz1102
Hi everyone, I have trouble depicting the difference between these two problems. The first problem uses the multiplication rule to solve while the second problem uses the counting rules (combination) to solve. To me, it seems like both problems could be solved using the multiplication rule so I don't understand why the second problem is solved using combination...

1.) Three cards are drawn from an ordinary deck and not replaced. Find the probability of these: a) getting 3 jacks.

Solution: P(3 jacks) = 4/52 * 3/51 * 2/50 = 1/5525

2.) Find the probability of getting 4 aces when 5 cards are drawn from an ordinary deck of cards.

Solution: P(4 aces) = 4C4 * 48 / 52C5 = 1*48/2,598,960 = 1/54,145

If I reword the second problem, I could reword it as the following:

Five cards are drawn from an ordinary deck. Find the probability of these: a) getting 4 aces.

Wouldn't this make it the exact same as problem #1, meaning I could solve #2 the same way I solved #1?

If you do it right. Remember there is one free card which can be anything. In addition as you draw the five cards in sequence, the free card may be in any position, so you have to add up five cases (actually multiply one case by 5, since the probabilities are all the same).

## 1. What is the multiplication rule in statistics?

The multiplication rule in statistics is a way to find the probability of two or more independent events occurring together. It states that the probability of two or more independent events occurring together is equal to the product of their individual probabilities.

## 2. How is the multiplication rule different from the addition rule?

The multiplication rule is used to find the probability of multiple independent events occurring together, while the addition rule is used to find the probability of at least one of multiple mutually exclusive events occurring. In other words, the multiplication rule involves finding the probability of events happening together, while the addition rule involves finding the probability of events happening separately.

## 3. What is the counting rule in statistics?

The counting rule, also known as the multiplication principle, is a way to find the total number of possible outcomes in a given situation. It states that if there are m ways to do one task and n ways to do another task, then there are m x n ways to do both tasks together.

## 4. How do I know when to use the multiplication rule or the counting rule?

The multiplication rule is used when finding the probability of multiple independent events occurring together, while the counting rule is used to find the total number of possible outcomes in a given situation. It is important to understand the difference between independent and mutually exclusive events in order to determine which rule to use.

## 5. Can the multiplication rule and the counting rule be used together?

Yes, the multiplication rule and the counting rule can be used together in certain situations. For example, if you need to find the probability of multiple independent events occurring together and the total number of possible outcomes, you can use both rules to solve the problem.

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